Simplify; express your answer in exponential form. Assume $t\neq 0, n\neq 0$. $\dfrac{{(t^{3})^{-5}}}{{(t^{3}n^{-5})^{4}}}$
Explanation: To start, try working on the numerator and the denominator independently. In the numerator, we have ${t^{3}}$ to the exponent ${-5}$ . Now ${3 \times -5 = -15}$ , so ${(t^{3})^{-5} = t^{-15}}$ In the denominator, we can use the distributive property of exponents. ${(t^{3}n^{-5})^{4} = (t^{3})^{4}(n^{-5})^{4}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(t^{3})^{-5}}}{{(t^{3}n^{-5})^{4}}} = \dfrac{{t^{-15}}}{{t^{12}n^{-20}}}$ Break up the equation by variable and simplify. $\dfrac{{t^{-15}}}{{t^{12}n^{-20}}} = \dfrac{{t^{-15}}}{{t^{12}}} \cdot \dfrac{{1}}{{n^{-20}}} = t^{{-15} - {12}} \cdot n^{- {(-20)}} = t^{-27}n^{20}$.